Generally there are two types of group.
There is the church/village/community hall type playgroup, though they maybe held in other places such as children's centres.
These are normally based on letting the kids play freely with the toys provided, with refreshments for kids and adults. Some will do a craft, some might have story time or songtime or another organised activity. Often these are run by volunteers, though not always, and often by the parents who attend. Be prepared to make an effort to chat, (if you want to meet people) and when anyone smiles or says hello, respond! Many people make lifelong friends at this type of group. These groups usually cost £2 or £3, and are usually pay as you go.
The other type are the planned activities. Baby gym, music sessions, baby massage, rhyme time at the local library, messy play, baby yoga, tots sports, etc etc.
These are sessions where a leader, runs an activity. If you are shy of meeting people, these might be better, as everyone is involved in an activity. They can however, sometimes cost £££'s. Sometimes need to be booked in advance, or you have to commit to the whole course or a number of sessions. However the leader is paid, and so it is his/her job to make sure everyone is happy.
(Library activities are normally free, of course)